British police have arrested five men after a video was posted on the internet that showed men mocking the deadly Grenfell Tower blaze by burning an effigy of the building as part of Guy Fawkes Night celebrations.

The video, which appeared on social media, showed a cardboard model of the tower with cut-outs of residents in the windows being set alight on a bonfire while those watching laughed and made jokes.

"To disrespect those who lost their lives at Grenfell Tower, as well as their families and loved ones, is utterly unacceptable," Prime Minister Theresa May said on Twitter.

The leader of the Grenfell Tower fire investigation, Metropolitan Police Commander Stuart Cundy, said he was "appalled by the callous nature of the video".

"To mock that disaster in such a crude way is vile," Mr Cundy said.

"I can't imagine the distress this video will undoubtedly cause to bereaved families and survivors."

Police said five men, aged 19, 46, 55 and two 49-year-olds, had been arrested on suspicion of a public order offence after handing themselves into a police station in south London.

Across Britain in early November, towns and villages hold annual firework parties and burn effigies of Guy Fawkes, the Roman Catholic plotter who tried to blow up parliament in 1605.

Larger celebrations often burn celebrity figures with effigies of flamboyant ex-foreign secretary Boris Johnson being torched at a number of events this year, while previous targets have included US President Donald Trump.